The usage of baby daddy varies from place to place. In many places, and I believe originally, it simply was a way to refer to a person who was the father of your child, but who was not currently your boyfriend or husband. Many baby daddies are involved with raising their child, provide financial support, and are what most Americans would simply call a father, and what in times past might be referred to as an 'ex-husband'. However, with the decrease in popularity of shotgun weddings, it is often the case that a baby daddy was never actually a husband, making that term inapplicable.
In this usage, it may be judgmental, but does not need to be. It does seem to be the case that this term is used in preference to 'father' with the intention of providing the additional information that the parents are not married; whether this is done simply because the term is in common usage, done in order to avoid lengthy explanations, or done just to cast shade depends on the…